Theoretical optimization of Irinotecan-based anticancer strategies in the case of drug-induced efflux

The anticancer drug Irinotecan (CPT11) is known to trigger the induction of ATP-Binding Cassette (ABC) transporters, responsible for the efflux of the drug and its metabolites outside of the cells. The drug-modulated overexpression of those transporters prevents its accumulation in the intracellular medium, therefore decreasing its efficacy. A critical clinical concern lies in the design of CPT11-based therapeutic strategies which eradicate a maximum number of cancer cells despite their ability to become resistant. In order to address this issue, we supplemented an existing mathematical model of CPT11 molecular pharmacokinetics–pharmacodynamics (PK–PD) with a new model of CPT11-induced overexpression of ABC transporters. We then theoretically optimized exposure to CPT11 given as a single agent or combined either with ABC transporter inhibitors, or with inhibitors of nuclear factors whose activation is responsible for transporter overexpression. We firstly considered a cancer cell population endowed with the ability of inducing their transporters. For any drug combination, we concluded that the highest concentration of CPT11 should be administered in order to kill a maximum number of cancer cells, despite the triggering of resistance. We then considered a population of healthy cells which were assumed to be identical to cancer cells except that they were not able to become resistant. Optimal schemes were defined as the ones which maximized DNA damage in cancer cells under the constraint of DNA damage in healthy cells not exceeding a tolerability threshold. The optimal therapeutic strategy consisted in combining CPT11 with ABC transporter inhibitors as it achieved a complete reversal of resistance by means of the lowest concentrations of CPT11.     

Explicit Formulas for the Green’s Function and the Bergman Kernel for Monogenic Functions in Annular Shaped Domains in {\mathbb{R}^{n+1}}

By applying a reflection principle we set up fully explicit representation formulas for the harmonic Green’s function for orthogonal sectors of the annulus of the unit ball of ${\mathbb{R}^n}$ . From the harmonic Green’s function we then can determine the Bergman kernel function of Clifford holomorphic functions by applying an appropriate vector differentiation. As a concrete application we give an explicit analytic representation formula of the solutions to an n-dimensional Dirichlet problem in annular shaped domains that arises in the context of heat conduction.     

Basics of a generalized Wiman–Valiron theory for monogenic Taylor series of finite convergence radius

In this paper, we develop the basic concepts for a generalized Wiman–Valiron theory for Clifford algebra valued functions that satisfy inside an n + 1-dimensional ball the higher dimensional Cauchy-Riemann system ${\frac{\partial f}{\partial x_0} + \sum_{i=1}^n e_i\frac{\partial f}{\partial x_i}=0}In this paper, we develop the basic concepts for a generalized Wiman–Valiron theory for Clifford algebra valued functions that satisfy inside an n + 1-dimensional ball the higher dimensional Cauchy-Riemann system \frac?f?x₀ + ?_i=1ⁿ e_i\frac?f?x_i=0{\frac{\partial f}{\partial x_0} + \sum_{i=1}^n e_i\frac{\partial f}{\partial x_i}=0} . These functions are called monogenic or Clifford holomorphic inside the ball. We introduce growth orders, the maximum term and a generalization of the central index for monogenic Taylor series of finite convergence radius. Our goal is to establish explicit relations between these entities in order to estimate the asymptotic growth behavior of a monogenic function in a ball in terms of its Taylor coefficients. Furthermore, we exhibit a relation between the growth order of such a function f and the growth order of its partial derivatives.     

Maximum Principle for the Regularized Schrödinger Operator

In this paper we present analogues of the maximum principle and of some parabolic inequalities for the regularized time-dependent Schrödinger operator on open manifolds using Günter derivatives. Moreover, we study the uniqueness of bounded solutions for the regularized Schrödinger–Günter problem and obtain the corresponding fundamental solution. Furthermore, we present a regularized Schrödinger kernel and prove some convergence results. Finally, we present an explicit construction for the fundamental solution to the Schrödinger–Günter problem on a class of conformally flat cylinders and tori.     

On the Navier–Stokes equations with free convection in three‐dimensional unbounded triangular channels

The quaternionic calculus is a powerful tool for treating the Navier–Stokes equations very elegantly and in a compact form, through the evaluation of two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. In this paper, we use special variants of quaternionic‐holomorphic multiperiodic functions in order to obtain explicit formulas for unbounded three‐dimensional parallel plate channels, rectangular block domains and regular triangular channels. Copyright © 2007 John Wiley & Sons, Ltd.     

Prediction and Validation of a Druggable Site on Virulence Factor of Drug Resistant Burkholderia cenocepacia**

Burkholderia cenocepacia is an opportunistic Gram-negative bacterium that causes infections in patients suffering from chronic granulomatous diseases and cystic fibrosis. It displays significant morbidity and mortality due to extreme resistance to almost all clinically useful antibiotics. The bacterial lectin BC2L-C expressed in B. cenocepacia is an interesting drug target involved in bacterial adhesion and subsequent deadly infection to the host. We solved the first high resolution crystal structure of the apo form of the lectin N-terminal domain (BC2L-C-nt) and compared it with the ones complexed with carbohydrate ligands. Virtual screening of a small fragment library identified potential hits predicted to bind in the vicinity of the fucose binding site. A series of biophysical techniques and X-ray crystallographic screening were employed to validate the interaction of the hits with the protein domain. The X-ray structure of BC2L-C-nt complexed with one of the identified active fragments confirmed the ability of the site computationally identified to host drug-like fragments. The fragment affinity could be determined by titration microcalorimetry. These structure-based strategies further provide an opportunity to elaborate the fragments into high affinity anti-adhesive glycomimetics, as therapeutic agents against B. cenocepacia.     

Photophysical properties of binuclear ruthenium(ii) bis(2,2':6',2''-terpyridine) complexes built around a central 2,2'-bipyrimidine receptor

A binuclear complex has been synthesized having ruthenium(ii) bis(2,2':6',2'-terpyridine) terminals attached to a central 2,2'-bipyrimidine unit via ethynylene groups. Cyclic voltammetry indicates that the substituted terpyridine is the most easily reduced subunit and the main chromophore involves charge transfer from the metal centre to this ligand. The resultant metal-to-ligand, charge-transfer (MLCT) triplet state is weakly emissive and has a lifetime of 60 ns in deoxygenated solution at room temperature. The luminescence yield and lifetime increase with decreasing temperature in a manner that indicates the lowest-energy MLCT triplet couples to at least two higher-energy triplets. Cations can bind to the central bipyrimidine unit, forming both 1:1 and 1:2 (ligand:metal) complexes as confirmed by electrospray MS analysis. The photophysical properties depend on the number of bound cations and on the nature of the cation. In the specific case of binding zinc(ii) cations, the 1:1 complex has a triplet lifetime of 8.0 ns while that of the 1:2 complex is 1.8 ns. The 1:1 complexes formed with Ba(2+) and Mg(2+) are more luminescent than is the parent compound while the 1:2 complexes are much less luminescent. It is shown that the coordinated cations raise the reduction potential of the central bipyrimidine unit and thereby increase the activation energy for coupling with the metal-centred state. Complexation also introduces a non-emissive intramolecular charge-transfer (ICT) state that couples to the lowest-energy MLCT triplet and provides an additional non-radiative decay route. The triplet state of the 1:2 complex formed with added Zn(2+) cations decays preferentially via this ICT state.     

Divalent Cations Increase DNA Repair Activities of Bacterial (6‐4) Photolyases

The (6‐4) photolyases of the FeS‐BCP group can be considered as the most ancient type among the large family of cryptochrome and photolyase flavoproteins. In contrast to other photolyases, they contain an Fe‐S cluster of unknown function, a DMRL chromophore, an interdomain loop, which could interact with DNA, and a long C‐terminal extension. We compared DNA repair and photoreduction of two members of the FeS‐BCP family, Agrobacterium fabrum PhrB and Rhodobacter sphaeroides RsCryB, with a eukaryotic (6‐4) photolyase from Ostreococcus, OsCPF, and a member of the class III CPD photolyases, PhrA from A. fabrum. We found that the low DNA repair effectivity of FeS‐BCP proteins is largely stimulated by Mg²⁺ and other divalent cations, whereas no effect of divalent cations was observed in OsCPF and PhrA. The (6‐4) repair activity in the presence of Mg²⁺ is comparable with the repair activities of the other two photolyases. The photoreduction, on the other hand, is negatively affected by Mg²⁺ in PhrB, but stimulated by Mg²⁺ in PhrA. A clear relationship of Mg²⁺ dependency on DNA repair with the evolutionary position conflicts with Mg²⁺ dependency of photoreduction. We discuss the Mg²⁺ effect in the context of structural data and DNA binding.     

Tuning the Surface of Nanoparticles: Impact of Poly(2‐ethyl‐2‐oxazoline) on Protein Adsorption in Serum and Cellular Uptake

Due to the adsorption of biomolecules, the control of the biodistribution of nanoparticles is still one of the major challenges of nanomedicine. Poly(2‐ethyl‐2‐oxazoline) (PEtOx) for surface modification of nanoparticles is applied and both protein adsorption and cellular uptake of PEtOxylated nanoparticles versus nanoparticles coated with poly(ethylene glycol) (PEG) and non‐coated positively and negatively charged nanoparticles are compared. Therefore, fluorescent poly(organosiloxane) nanoparticles of 15 nm radius are synthesized, which are used as a scaffold for surface modification in a grafting onto approach. With multi‐angle dynamic light scattering, asymmetrical flow field‐flow fractionation, gel electrophoresis, and liquid chromatography‐mass spectrometry, it is demonstrated that protein adsorption on PEtOxylated nanoparticles is extremely low, similar as on PEGylated nanoparticles. Moreover, quantitative microscopy reveals that PEtOxylation significantly reduces the non‐specific cellular uptake, particularly by macrophage‐like cells. Collectively, studies demonstrate that PEtOx is a very effective alternative to PEG for stealth modification of the surface of nanoparticles.